Theorem fneq1i 5421

Description: Equality inference for function predicate with domain. (Contributed by Paul Chapman, 22-Jun-2011.)

Hypothesis

Ref	Expression
fneq1i.1	|- F = G

Assertion

Ref	Expression
fneq1i	|- ( F Fn A <-> G Fn A )

Proof of Theorem fneq1i

Step	Hyp	Ref	Expression
1		fneq1i.1	. 2 |- F = G
2		fneq1 5415	. 2 |- ( F = G -> ( F Fn A <-> G Fn A ) )
3	1, 2	ax-mp 5	1 |- ( F Fn A <-> G Fn A )

Syntax hints:   <-> wb 105   = wceq 1395   Fn wfn 5319

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-io 714  ax-5 1493  ax-7 1494  ax-gen 1495  ax-ie1 1539  ax-ie2 1540  ax-8 1550  ax-10 1551  ax-11 1552  ax-i12 1553  ax-bndl 1555  ax-4 1556  ax-17 1572  ax-i9 1576  ax-ial 1580  ax-i5r 1581  ax-ext 2211

This theorem depends on definitions:  df-bi 117  df-3an 1004  df-tru 1398  df-nf 1507  df-sb 1809  df-clab 2216  df-cleq 2222  df-clel 2225  df-nfc 2361  df-v 2802  df-un 3202  df-in 3204  df-ss 3211  df-sn 3673  df-pr 3674  df-op 3676  df-br 4087  df-opab 4149  df-rel 4730  df-cnv 4731  df-co 4732  df-dm 4733  df-fun 5326  df-fn 5327

This theorem is referenced by:  fnunsn  5436  fnopabg  5453  f1oun  5600  f1oi  5619  f1osn  5621  ovid  6133  tfri1d  6496  frec2uzrand  10657  frec2uzf1od  10658  frecfzennn  10678  xnn0nnen  10689  prdsinvlem  13681  dfrelog  15574  edgstruct  15905  nninfsellemeqinf  16554